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Wang X, Bongiovanni D, Wang Z, Abdrabou A, Hu Z, Jukić D, Song D, Morandotti R, El-Ganainy R, Chen Z, Buljan H. Construction of Topological Bound States in the Continuum Via Subsymmetry. ACS PHOTONICS 2024; 11:3213-3220. [PMID: 39184183 PMCID: PMC11342891 DOI: 10.1021/acsphotonics.4c00600] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [Grants] [Track Full Text] [Figures] [Subscribe] [Scholar Register] [Received: 03/29/2024] [Revised: 06/27/2024] [Accepted: 06/27/2024] [Indexed: 08/27/2024]
Abstract
Topological bound states in the continuum (BICs) are localized topological boundary modes coexisting with a continuous spectrum of extended modes. They have been realized in systems with symmetry-protected topological phases, where their immunity to defects and perturbations depends on the presence of symmetries. Here we propose a method that transforms an in-gap topological boundary state into a BIC by using the concept of subsymmetry. We design the coupling between a system possessing in-gap topological modes and a system possessing a continuum of states that results in topological BICs. We define the criteria for the coupling that yields the desired results. To implement this scheme, we construct representative topological BICs based on one-dimensional Su-Schrieffer-Heeger models and implement them in photonic lattices. Our results not only reveal novel physical phenomena but may also provide methods for designing a new generation of topological devices.
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Affiliation(s)
- Xiangdong Wang
- TEDA
Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Domenico Bongiovanni
- TEDA
Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- INRS-EMT, 1650 Blvd.
Lionel-Boulet, Varennes, Quebec J3X 1S2, Canada
| | - Ziteng Wang
- TEDA
Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Amgad Abdrabou
- Elmore
Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, Indiana 47907, United States
| | - Zhichan Hu
- TEDA
Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Dario Jukić
- Faculty
of Civil Engineering, University of Zagreb, A. Kačića Miošića
26, Zagreb 10000, Croatia
| | - Daohong Song
- TEDA
Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Collaborative
Innovation Center of Extreme Optics, Shanxi
University, Taiyuan, Shanxi 030006, China
| | | | - Ramy El-Ganainy
- Department
of Physics, Michigan Technological University, Houghton, Michigan 49931, United States
| | - Zhigang Chen
- TEDA
Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Collaborative
Innovation Center of Extreme Optics, Shanxi
University, Taiyuan, Shanxi 030006, China
| | - Hrvoje Buljan
- TEDA
Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Department
of Physics, Faculty of Science, University
of Zagreb, Bijenička
c. 32, Zagreb 10000, Croatia
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Abstract
The topological properties of an object, associated with an integer called the topological invariant, are global features that cannot change continuously but only through abrupt variations, hence granting them intrinsic robustness. Engineered metamaterials (MMs) can be tailored to support highly nontrivial topological properties of their band structure, relative to their electronic, electromagnetic, acoustic and mechanical response, representing one of the major breakthroughs in physics over the past decade. Here, we review the foundations and the latest advances of topological photonic and phononic MMs, whose nontrivial wave interactions have become of great interest to a broad range of science disciplines, such as classical and quantum chemistry. We first introduce the basic concepts, including the notion of topological charge and geometric phase. We then discuss the topology of natural electronic materials, before reviewing their photonic/phononic topological MM analogues, including 2D topological MMs with and without time-reversal symmetry, Floquet topological insulators, 3D, higher-order, non-Hermitian and nonlinear topological MMs. We also discuss the topological aspects of scattering anomalies, chemical reactions and polaritons. This work aims at connecting the recent advances of topological concepts throughout a broad range of scientific areas and it highlights opportunities offered by topological MMs for the chemistry community and beyond.
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Affiliation(s)
- Xiang Ni
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- School of Physics and Electronics, Central South University, Changsha, Hunan 410083, China
| | - Simon Yves
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
| | - Alex Krasnok
- Department of Electrical and Computer Engineering, Florida International University, Miami, Florida 33174, USA
| | - Andrea Alù
- Photonics Initiative, Advanced Science Research Center, City University of New York, New York, New York 10031, United States
- Department of Electrical Engineering, City College, The City University of New York, 160 Convent Avenue, New York, New York 10031, United States
- Physics Program, The Graduate Center, The City University of New York, 365 Fifth Avenue, New York, New York 10016, United States
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3
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Bongiovanni D, Jukić D, Hu Z, Lunić F, Hu Y, Song D, Morandotti R, Chen Z, Buljan H. Dynamically Emerging Topological Phase Transitions in Nonlinear Interacting Soliton Lattices. PHYSICAL REVIEW LETTERS 2021; 127:184101. [PMID: 34767391 DOI: 10.1103/physrevlett.127.184101] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.3] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 03/15/2021] [Accepted: 09/13/2021] [Indexed: 06/13/2023]
Abstract
We demonstrate dynamical topological phase transitions in evolving Su-Schrieffer-Heeger lattices made of interacting soliton arrays, which are entirely driven by nonlinearity and thereby exemplify an emergent nonlinear topological phenomenon. The phase transitions occur from the topologically trivial-to-nontrivial phase in periodic succession with crossovers from the topologically nontrivial-to-trivial regime. The signature of phase transition is the gap-closing and reopening point, where two extended states are pulled from the bands into the gap to become localized topological edge states. Crossovers occur via decoupling of the edge states from the bulk of the lattice.
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Affiliation(s)
- Domenico Bongiovanni
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, Quebec J3X 1S2, Canada
| | - Dario Jukić
- Faculty of Civil Engineering, University of Zagreb, A. Kačića Miošića 26, 10000 Zagreb, Croatia
| | - Zhichan Hu
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Frane Lunić
- Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000 Zagreb, Croatia
| | - Yi Hu
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Daohong Song
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
| | - Roberto Morandotti
- INRS-EMT, 1650 Boulevard Lionel-Boulet, Varennes, Quebec J3X 1S2, Canada
- Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, Sichuan 610054, China
| | - Zhigang Chen
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Department of Physics and Astronomy, San Francisco State University, San Francisco, California 94132, USA
| | - Hrvoje Buljan
- The MOE Key Laboratory of Weak-Light Nonlinear Photonics, TEDA Applied Physics Institute and School of Physics, Nankai University, Tianjin 300457, China
- Department of Physics, Faculty of Science, University of Zagreb, Bijenička c. 32, 10000 Zagreb, Croatia
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Qi F, Wang YF, Ma QY, Zheng WH. Experimentally simulating quantum walks with self-collimated light. Sci Rep 2016; 6:28610. [PMID: 27353428 PMCID: PMC4926089 DOI: 10.1038/srep28610] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.9] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 01/07/2016] [Accepted: 06/06/2016] [Indexed: 11/10/2022] Open
Abstract
In self-collimated photonic crystal, periodically arranged air holes of sub-wavelength scale provide flattened equi-frequency curves perpendicular to the ΓM direction, which allow light or photons propagating in a quasi-uniform medium without diffraction. Here we for the first time experimentally simulate four-step single-photon discrete time quantum walks with classical light in such a photonic crystal chip fabricated on silicon-on-insulator. Similarities between theoretical expectations and experimental results are higher than 0.98. The functional area is compact and can be extended to construct more complicated linear quantum circuits.
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Affiliation(s)
- F Qi
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, CAS, No. 35A, Qinghua East Road, Haidian District, Beijing, Post Code: 100083, China.,Laboratory of Solid State Optoelectronics Information Technology, Institute of Semiconductors, CAS, No. 35A, Qinghua East Road, Haidian District, Beijing, Post Code: 100083, China.,College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, Post Code: 100049, China
| | - Y F Wang
- Laboratory of Solid State Optoelectronics Information Technology, Institute of Semiconductors, CAS, No. 35A, Qinghua East Road, Haidian District, Beijing, Post Code: 100083, China
| | - Q Y Ma
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, CAS, No. 35A, Qinghua East Road, Haidian District, Beijing, Post Code: 100083, China.,Laboratory of Solid State Optoelectronics Information Technology, Institute of Semiconductors, CAS, No. 35A, Qinghua East Road, Haidian District, Beijing, Post Code: 100083, China.,College of Materials Science and Opto-Electronic Technology, University of Chinese Academy of Sciences, No. 19A Yuquan Road, Beijing, Post Code: 100049, China
| | - W H Zheng
- State Key Laboratory on Integrated Optoelectronics, Institute of Semiconductors, CAS, No. 35A, Qinghua East Road, Haidian District, Beijing, Post Code: 100083, China.,Laboratory of Solid State Optoelectronics Information Technology, Institute of Semiconductors, CAS, No. 35A, Qinghua East Road, Haidian District, Beijing, Post Code: 100083, China
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Malzard S, Poli C, Schomerus H. Topologically Protected Defect States in Open Photonic Systems with Non-Hermitian Charge-Conjugation and Parity-Time Symmetry. PHYSICAL REVIEW LETTERS 2015; 115:200402. [PMID: 26613422 DOI: 10.1103/physrevlett.115.200402] [Citation(s) in RCA: 58] [Impact Index Per Article: 6.4] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Received: 06/08/2015] [Indexed: 06/05/2023]
Abstract
We show that topologically protected defect states can exist in open (leaky or lossy) systems even when these systems are topologically trivial in the closed limit. The states appear from within the continuum, thus in the absence of a band gap, and are generated via exceptional points (a spectral transition that occurs in open wave and quantum systems with a generalized time-reversal symmetry), or via a degeneracy induced by charge-conjugation symmetry (which is related to the pole transition of Majorana zero modes). We demonstrate these findings for a leaking passive coupled-resonator optical waveguide with asymmmetric internal scattering, where the required symmetries (non-Hermitian versions of time-reversal symmetry, chirality, and charge conjugation) emerge dynamically.
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Affiliation(s)
- Simon Malzard
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Charles Poli
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
| | - Henning Schomerus
- Department of Physics, Lancaster University, Lancaster LA1 4YB, United Kingdom
- Max-Planck-Institut für Physik komplexer Systeme, 01187 Dresden, Germany
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Poli C, Bellec M, Kuhl U, Mortessagne F, Schomerus H. Selective enhancement of topologically induced interface states in a dielectric resonator chain. Nat Commun 2015; 6:6710. [PMID: 25833814 PMCID: PMC4396359 DOI: 10.1038/ncomms7710] [Citation(s) in RCA: 110] [Impact Index Per Article: 12.2] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/29/2014] [Accepted: 02/19/2015] [Indexed: 11/17/2022] Open
Abstract
The recent realization of topological phases in insulators and superconductors has advanced the search for robust quantum technologies. The prospect to implement the underlying topological features controllably has given incentive to explore optical platforms for analogous realizations. Here we realize a topologically induced defect state in a chain of dielectric microwave resonators and show that the functionality of the system can be enhanced by supplementing topological protection with non-hermitian symmetries that do not have an electronic counterpart. We draw on a characteristic topological feature of the defect state, namely, that it breaks a sublattice symmetry. This isolates the state from losses that respect parity-time symmetry, which enhances its visibility relative to all other states both in the frequency and in the time domain. This mode selection mechanism naturally carries over to a wide range of topological and parity-time symmetric optical platforms, including couplers, rectifiers and lasers. At interfaces between systems with topologically distinct band structure, robust symmetry protected states emerge. Here, Poli et al. control such states in a coupled dielectric resonator chain with parity-time symmetry and exploit their topological nature to protect them from absorptive losses.
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Affiliation(s)
- Charles Poli
- Department of Physics, Lancaster University, Lancaster LA1 4YB, UK
| | - Matthieu Bellec
- Laboratoire de Physique de la Matière Condensée, CNRS UMR 7336, Université Nice Sophia Antipolis, 06100 Nice, France
| | - Ulrich Kuhl
- Laboratoire de Physique de la Matière Condensée, CNRS UMR 7336, Université Nice Sophia Antipolis, 06100 Nice, France
| | - Fabrice Mortessagne
- Laboratoire de Physique de la Matière Condensée, CNRS UMR 7336, Université Nice Sophia Antipolis, 06100 Nice, France
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Photonic lattice simulation of dissipation-induced correlations in bosonic systems. Sci Rep 2015; 5:8438. [PMID: 25708778 PMCID: PMC4338417 DOI: 10.1038/srep08438] [Citation(s) in RCA: 10] [Impact Index Per Article: 1.1] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 10/29/2014] [Accepted: 01/19/2015] [Indexed: 11/21/2022] Open
Abstract
We propose an optical simulation of dissipation-induced correlations in one-dimensional (1D) interacting bosonic systems, using a two-dimensional (2D) array of linear photonic waveguides and only classical light. We show that for the case of two bosons in a 1D lattice, one can simulate on-site two-body dissipative dynamics using a linear 2D waveguide array with lossy diagonal waveguides. The intensity distribution of the propagating light directly maps out the wave function, allowing one to observe the dissipation-induced correlations with simple measurements. Beyond the on-site model, we also show that a generalised model containing nearest-neighbour dissipative interaction can be engineered and probed in the proposed set-up.
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8
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Angelakis DG, Das P, Noh C. Probing the topological properties of the Jackiw-Rebbi model with light. Sci Rep 2014; 4:6110. [PMID: 25130953 PMCID: PMC4135337 DOI: 10.1038/srep06110] [Citation(s) in RCA: 16] [Impact Index Per Article: 1.6] [Reference Citation Analysis] [Abstract] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 06/03/2014] [Accepted: 07/30/2014] [Indexed: 11/17/2022] Open
Abstract
The Jackiw-Rebbi model describes a one-dimensional Dirac field coupled to a soliton field and can be equivalently thought of as a model describing a Dirac field with a spatially dependent mass term. Neglecting the dynamics of the soliton field, a kink in the background soliton profile yields a topologically protected zero-energy mode for the field, which in turn leads to charge fractionalisation. We show here that the model, in the first quantised form, can be realised in a driven slow-light setup, where photons mimic the Dirac field and the soliton field can be implemented–and tuned–by adjusting optical parameters such as the atom-photon detuning. Furthermore, we discuss how the existence of the zero-mode and its topological stability can be probed naturally by studying the transmission spectrum. We conclude by analysing the robustness of our approach against possible experimental errors in engineering the Jackiw-Rebbi Hamiltonian in this optical setup.
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Affiliation(s)
- Dimitris G Angelakis
- 1] Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117543 Singapore [2] School of Electronic and Computer Engineering, Technical University of Crete, Chania, Crete, 73100 Greece
| | - P Das
- Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117543 Singapore
| | - C Noh
- Centre for Quantum Technologies, National University of Singapore, 2 Science Drive 3, 117543 Singapore
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